how does a GSM or CDMA service provider know that a phone is switched off or it is out-of-coverage area?

is there a protocol that says that when a phone is switched off it has to tell the tower that it is being switched off or is it a very weak signal that indicates out-of-coverage area while no signal indicates switched off?

in case it is the former, then what happens if the phone battery is removed. then is it switched off or out-of-coverage!